\xiti

\begin{xiaotis}

\xiaoti{计算：}
\begin{xiaoxiaotis}

    \begin{tblr}{columns={18em, colsep=0pt}}
        \xxt{$a^7 \div a^4$；} & \xxt{$x^{10} \div x^5$；} \\
        \xxt{$y^8 \div y^8$；} & \xxt{$(-5)^6 \div (-5)^3$；} \\
        \xxt{$(ax)^5 \div (ax)^3$；} & \xxt{$\left(-\dfrac{1}{2}y\right)^4 \div \left(-\dfrac{1}{2}y\right)$；} \\
        \xxt{$a^{3n} \div a^n$；} & \xxt{$x^{2n+1} \div x^{n+1}$；} \\
        \xxt{$(a^2)^m \div a^m$；} & \xxt{$t^6 \div (t^4 \div t^3)$；} \\
        \xxt{$a^2 \cdot (a^2)^3 \div a^4$；} & \xxt{$(a + b)^3 \div (a + b)^2 \cdot (a + b)^4$。}
    \end{tblr}

\end{xiaoxiaotis}

\xiaoti{计算：}
\begin{xiaoxiaotis}

    \begin{tblr}{columns={18em, colsep=0pt}}
        \xxt{$-12a^5b^3c \div (-3a^2b)$；} & \xxt{$42x^6y^8 \div (-3x^2y)^3$；} \\
        \xxt{$24x^2y^5 \div (-6x^2y^3)$；} & \xxt{$-25t^8k \div (-5t^5k)$；} \\
        \xxt{$(-5r^2c)^2 \div 5r^4c$；} & \xxt{$7m^2(4m^3p) \div 7m^5$；} \\
        \xxt{$-45(u^3v^4)^2 \div 5u^5v^4$；} & \xxt{$-12(s^4t^3)^3 \div \left(\dfrac{1}{2}s^2t^3\right)^2$；} \\
        \xxt{$(-5r^2st^3)^2 (-2rs^2t)^3$；} & \xxt{$(2a^2bc)^3 \left(\dfrac{1}{2}ab^3c^2\right)^5$；} \\
        \SetCell[c=2]{} \xxt{$(-38x^4y^5z) \div 19xy^5 \cdot \left(-\dfrac{3}{4}x^3y^2\right)$；} \\
        \SetCell[c=2]{} \xxt{$(2ax)^2 \cdot \left(-\dfrac{2}{5}a^4x^3y^3\right) \div \left(-\dfrac{1}{2}a^5xy^2\right)$。}
    \end{tblr}

\end{xiaoxiaotis}

\xiaoti{一颗人造地球卫星的速度是 $2.88 \times 10^7 \text{米/时}$，一架喷气式飞机的速度是 $1.8 \times 10^6 \text{米/时}$，
    这颗人造地球卫星的速度是这架喷气式飞机的速度的多少倍？
}

\begin{enhancedline}
\xiaoti{计算：}
\begin{xiaoxiaotis}

    \xxt{$(6x^4 - 8x^3) \div (-2x^2)$；}

    \xxt{$(8a^3b - 5a^2b^2) \div 4ab$；}

    \xxt{$(12x^3 - 8x^2 + 16x) \div 4x$；}

    \xxt{$\left(\dfrac{2}{5}y^3 - 7xy^2 + \dfrac{2}{3}y^5\right) \div \dfrac{2}{3}y^2$；}

    \xxt{$(9a^3x^5 - 6a^2x^4 + 15a^4x^3) \div (-3a^2x^3)$；}

    \xxt{$[28x^7y^3 - 21x^5y^5 + 2y(7x^3y^3)^2] \div 7x^5y^3$；}

    \xxt{$\left(0.25a^3b^2 - \dfrac{1}{2}a^4b^5 - \dfrac{1}{6}a^5b^3\right) \div (-0.5a^3b^2)$；}

    \xxt{$(3a^{n+1} + 6a^{n+2} - 9a^n) \div 3a^{n-1}$。}

\end{xiaoxiaotis}


\xiaoti{化简：}
\begin{xiaoxiaotis}

    \xxt{$[(2x + y)^2 - y(y + 4x)] \div 2x$；}

    \xxt{$[(3x + 2y)(3x - 2y) - (x + 2y)(5x - 2y)] \div 4x$；}

    \xxt{$\left[\left(4x - \dfrac{1}{2}y\right)^2 + 4y\left(x - \dfrac{y}{16}\right)\right] \div 8x^2$；}

    \xxt{$\left[(-3xy)^2 \cdot x^3 - 2x^2 \cdot (3xy^2)^3 \cdot \dfrac{1}{2}y\right] \div 9x^4y^2$。}

\end{xiaoxiaotis}

\xiaoti{计算：}
\begin{xiaoxiaotis}

    \xxt{$(2x^2 + 23x + 56) \div (2x + 7)$；}

    \xxt{$(2x^3 + 27x - 12x^2 - 27) \div (x - 3)$；}

    \xxt{$(5x^3 + 9x^2 + 10x + 5) \div (x^2 + x + 1)$；}

    \xxt{$(2y^4 - y^3 + y - 3) \div (3 - 2y + y^2)$。}

\end{xiaoxiaotis}
\end{enhancedline}

\xiaoti{长方形的面积是 $a^2 - 3ab + 2b^2$，它的一条边长是 $a - b$，求它的周长。}

\xiaoti{已知除式、商式及余式，求被除式。}
\begin{xiaoxiaotis}

    \xxt{$\text{除式} = 6x^2 + 3x - 5$， $\text{商式} = 4x - 5$， $\text{余式} = -8$；}

    \xxt{$\text{除式} = -2x^2 -x + 1$， $\text{商式} = x^2 - 2$， $\text{余式} = 3x + 7$。}

\end{xiaoxiaotis}

\end{xiaotis}

